Using a sharp knife, trim away as much of the surface fat from the lamb as possible. Brush or rub the chops on both sides with olive oil, and season generously with salt and pepper.
Press the parsley and basil firmly into both sides of each chop. Let stand at room temperature for 20 to 30 minutes before roasting.
Preheat an oven to 450 degrees F.
Meanwhile, start making the sauce: In a small saucepan over medium-low heat, warm the olive oil. Add the shallot and saute until softened, 3 to 4 minutes. Add the garlic and cook for 1 minute.
Increase the heat to medium-high, add the tomatoes and cook, stirring frequently, until the tomatoes soften and release their liquid, 3 to 4 minutes.
Add the vinegar and season with salt and pepper. Cook until most of the liquid has evaporated, 3 to 4 minutes.
Remove from heat, stir in the basil and mint, and set aside until the lamb chops are roasted.
Preheat a large, heavy ovenproof fry pan over high heat until very hot. Add the 1 Tb olive oil, and then add the lamb chops and sear for 2 minutes. Turn the chops and sear for 1 minute on the other side.
Immediately transfer the pan to the oven and roast the lamb until an instant-read thermometer inserted into the thickest part of the meat, away from the bone, registers 125 to 130 F for medium-rare, 5 to 6 minutes.
Remove the pan from the oven, transfer the chops to a warmed platter and cover loosely with aluminum foil. Let rest while you finish the sauce.
Pour off any excess fat from the pan. Set the pan over medium-high heat, pour in the wine and cook, stirring to scrape up the browned bits from the pan bottom.
Add the tomato sauce and any juices that have accumulated on the platter and bring to a boil. Remove from the heat.
Divide the chops among warmed plates. Divide the sauce evenly among them, spooning it over the top. Serve immediately.